Simplify the following expression: $a = \dfrac{z - 9}{8} \div \dfrac{5z}{7}$
Solution: Dividing by an expression is the same as multiplying by its inverse. $a = \dfrac{z - 9}{8} \times \dfrac{7}{5z}$ When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ (z - 9) \times 7 } { 8 \times 5z}$ $a = \dfrac{7z - 63}{40z}$